Announcement for Prospective Students: The first unit on limits will be shortened by two weeks in the Spring 2020 offering of the course. This will allow for 3 full weeks where we do not learn any new material. Instead, we will solely focus on practicing for the exam. AP Calculus AB Exam Date: May 14, 2019 8 am Test Format: Section I: Multiple Choice | 45 Questions | 105 minutes | 50% of Exam Score • Part A: 28 questions; 55 minutes (no calculator permitted) • Part B: 17 questions; 50 minutes (graphing calculator permitted) Section II: Free (Constructed) Response | 6 Questions | 90 minutes | 50% of Exam Score • Part A: 2 problems; 30 minutes (graphing calculator permitted) • Part B: 4 problems; 1 hour (no calculator permitted) Updated 2019 AP Calculus AB Framework and Exam Description Week 1 (Unit 1: Limits)What is Calculus? 2.1 Average Rates of Change 2.1 Numerical Limit 2.2 Definition of a Limit 2.2 One Sided Limits vs. Two Sided Limits 2.3 Limit Rules 2.3 Limits Laws Week 2 (Unit 1: Limits)2.2 Graphical Limits Review of Polynomial Division 2.3 Limits of Polynomials and Rational Functions pg. 97 Techniques of Finding Limits - Direct Substitution
- Cancellation (Factoring)
- Radical Conjugate
- Algebraic Manipulation
- Making use of the formal definition of an absolute values
Week 3 (Unit 1: Limits)2.2 Infinite Limits (Sign Analysis/Limit Analysis) 2.6 Limits at Infinity Special Limit: lim as x->inf 1/x = 0 2.6 Horizontal Asymptotes 2.2 Asymptotes Week 4 (Unit 1: Limits)SNOW DAYReview of Exponentials and Logarithms Piece-wise Functions 2.3 Squeeze Theorem pg. 101 Week 5 (Unit 1: Limits)Review of Domain and Range 2.5 Continuity 2.5 Combinations of Continuous Functions pg. 117 2.5 Library of Continuous Functions pg. 120 Theorem 7 2.5 Intermediate Value Theorem pg. 122 Exam 1 on Monday February 11, 2019 (Practice Exam) Week 6 (Unit 2: Derivatives)2.7 Derivatives by Definition 2.8 Equations of Tangent Lines 3.1 Derivative Rules Week 7 (Unit 2: Derivatives)3.2 The Product Rule 3.2 The Quotient Rule Week 8 (Unit 2: Derivatives)Special Derivative: The derivative of ln(x) is 1/x 3.3 Trigonometric Derivatives 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithms & Logarithmic Differentiation as a technique Week 9 (Unit 2: Derivatives)Inverse Trigonometric Derivatives Equations of Normal Lines Related Rates (NOT ON EXAM 2) Unit 2 Exam Thursday March 7, 2019Week 10 (Unit 3: Derivatives Applications)Related Rates Extreme Value Theorem Critical Numbers Week 11 (Unit 3: Derivatives Applications)Extreme Values: Global (Absolute) vs. Local (Relative) 4.2 Mean Value Theorem 4.3 First Derivative Test for Local Extrema Finding Absolute Extrema Week 12 (Unit 3: Derivatives Applications)4.3 Second Derivative Test 4.3 Concavity 4.3 Inflection Points 4.3 Find Local Extrema 4.3 & 4.5 Curve Sketching 4.4 L'Hopitals Rule & Indeterminant Forms 4.7 Optimization Week 13 (Unit 4: Anti-Differentiation & Integrals)Unit 3 Exam 4.8 Anti-Derivatives Anti-Derivative S-V-A Word Problems Week 14 (Unit 4: Integrals)Unit 2 Test Re-Take and Review 5.1 Upper, Lower, Midpoint (7.7), Left-Hand, and Right-Hand Sums (Riemann Sums) Integral Notation 5.2 Integrals as Area 5.2 Definite Integrals 5.2 Properties of Integrable Functions pg. 385-387 5.3 Fundamental Theorem of Calculus (Part II) 5.4 Indefinite Integrals and Net Change Theorem Distinguish between Total (Unsigned) Area and Net (Signed) Area. (Remember, integral notation refers to signed/net area)6.5 Average Value of a Function Week 15 (Unit 4: Integrals & Unit 5 Integral Applications)5.3 Fundamental Theorem of Calculus (Part I) [And methods for adjusting limits of integration so that FTC I applies) 5.5 Substitution (Also called u-substitution) 7.7 Trapezoidal Sums (The last sum approximation that we will learn. Ignore everything else in this chapter that is not the midpoint or trapezoidal rule) 9.3 Separation of Variables (Only worry about the technique for the class example in this chapter) Review: Calculator Use for: Week 16 (Unit 5 Integral Applications & Course Review)Monday Unit 4 Exam April 29, 20196.1 Area Between Curves 6.2 Volumes of Solids and Cross Sections Wednesday Unit 5 Exam May 1, 20199.2 Review: Slope Fields Review: Limits of Composite Functions Review: Special Cases where Derivatives fail to exist (pg. 158) Week 17 (Course Review & Full Practice Exams)Week 18 (Exam Week)A.P. Calculus AB Exam May 14, 2019 8 am |